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5.2 Arity

In a sentence like PvQ, we said that P and Q are the inputs, and the complex sentence PvQ is the output.

Arity: the number of inputs a connective takes.

The number of inputs a connective has is called its arity.

If a connective takes one input, it is called unary. If it takes two inputs, it is called binary.

“Arity” is just a funny word made from the suffix of these words to stand for the general concept.

Unary: a connective with 1 input.
Binary: a connective with two inputs.

You can have connectives with three or more inputs too, which we will discuss in a later chapter.

Conjunction and disjunction connect two sentences together to make a complex sentence, so they are binary. (Remember, technically v and & connect two sentences, even though we allow a long string of “&”s or a long string of “v”s.)

Negation is unary, but remember that we still call it a connective!

A connective’s arity is fixed: ~ is always unary; & and v are always binary. (Even in P&Q&R, we call & binary.)